On the weighted fractional Poincare-type inequalities

TL;DR

This paper establishes weighted fractional Poincaré inequalities on John domains, where weights depend on boundary proximity and a compact boundary set, advancing understanding of fractional inequalities in weighted geometric contexts.

Contribution

It introduces new weighted fractional Poincaré inequalities on John domains with boundary-dependent weights, extending previous results to more general settings.

Findings

Proved weighted fractional Poincaré inequalities on John domains.

Established inequalities with weights depending on boundary distance.

Extended fractional inequality theory to more general weighted domains.

Abstract

Weighted fractional Poincar\'e-type inequalities are proved on John domains whenever the weights defined on the domain are depending on the distance to the boundary and to an arbitrary compact set in the boundary of the domain.